Domain Composition Method for Structural Optimization

2014 ◽  
Author(s):  
Wei Song ◽  
Hae Chang Gea ◽  
Bin Zheng
Keyword(s):  
Sensitivity Analysis ◽  
Topology Optimization ◽  
Structural Optimization ◽  
Design Domain ◽  
Material Distribution ◽  
Numerical Examples ◽  
Composition Method ◽  
Domain Composition ◽  
Fixed Design ◽  
Design Requirements

Conventionally, design domain of topology optimization is predefined and is not adjusted in the design optimization process since designers are required to specify the design domain in advance. However, it is difficult for a fixed design domain to satisfy design requirements such as domain sizing adjustment or boundaries change. In this paper, Domain Composition Method (DCM) for structural optimization is presented and it deals with the design domain adjustment and the material distribution optimization in one framework. Instead of treating design domain as a whole, DCM divides domain into several subdomains. Additional scaling factors and subdomain transformations are applied to describe changes between different designs. It then composites subdomains and solve it as a whole in the updated domain. Based on the domain composition, static analysis with DCM and sensitivity analysis are derived. Consequently, the design domain and the topology of the structure are optimized simultaneously. Finally, the effectiveness of the proposed DCM for structural optimization is demonstrated through different numerical examples.

Research of Topology Optimization of Nodal Density Based on Bilinear Interpolation

2015 ◽  
Vol 713-715 ◽  
pp. 1825-1829
Author(s):  
Yi Xian Du ◽  
Shuang Qiao Yan ◽  
Huang Hai Xie ◽  
Yan Zhang ◽  
Qi Hua Tian
Keyword(s):  
Topology Optimization ◽  
Density Field ◽  
Design Domain ◽  
Checkerboard Pattern ◽  
Bilinear Interpolation ◽  
Fixed Design ◽  
Numerical Instabilities ◽  
Nature Of Mathematics ◽  
Nodal Density ◽  
Smooth Density

With the purpose to overcome the numerical instabilities and to generate more distinct structural layouts in the topology optimization, by using bilinear interpolation function, a topology optimization model of density interpolation based on nodal density is established, smooth density field is constructed. This method can ensure that the density field in the fixed design domain owns C0 continuity, and checkerboard patterns are naturally avoided in the nature of mathematics. After adding the sensitivity filtering, the optimal structures are smoother and have lesser details, which is helpful for manufacturing. Two numerical examples show that not only checkerboard pattern can be solved by the proposed method, but also the middle density nodal can be suppressed effectively.

Topology Optimization for Steady-State Heat Transfer Problems Including Design-Dependent Effects

2008 ◽  
Author(s):  
Atsuro Iga ◽  
Shinji Nishiwaki ◽  
Kazuhiro Izui ◽  
Masataka Yoshimura
Keyword(s):  
Heat Transfer ◽  
Topology Optimization ◽  
Optimization Method ◽  
Homogenization Method ◽  
Heaviside Function ◽  
Design Domain ◽  
Transfer Coefficients ◽  
Total Potential ◽  
Fixed Design ◽  
Topology Optimization Method

In this paper, a topology optimization method is constructed for thermal problems with generic heat transfer boundaries in a fixed design domain that includes design-dependent effects. First, the topology optimization method for thermal problems is briefly explained using a homogenization method for the relaxation of the design domain, where a continuous material distribution is assumed, to suppress numerical instabilities and checkerboards. Next, a method is developed for handling heat transfer boundaries between material and void regions that appear in the fixed design domain and move during the optimization process, using the Heaviside function as a function of node-based material density to extract the boundaries of the target structure being optimized so that the heat transfer boundary conditions can be set. Shape dependencies concerning heat transfer coefficients are also considered in the topology optimization scheme. The optimization problem is formulated using the concept of total potential energy and an optimization algorithm is constructed using the Finite Element Method and Sequential Linear Programming. Finally, several numerical examples are presented to confirm the usefulness of the proposed method.

Architectural Morphogenesis Through Topology Optimization

2018 ◽  
pp. 69-92 ◽  
Author(s):  
Roberto Naboni ◽  
Ingrid Paoletti
Keyword(s):  
Topology Optimization ◽  
Structural Optimization ◽  
Structural Design ◽  
Cellular Materials ◽  
Design Domain ◽  
Main Approach ◽  
Cellular Solid ◽  
Automotive Engineering ◽  
Optimization Of Microstructures ◽  
Wasted Energy

This chapter illustrates the main approach for a generative use of structural optimization in architecture. Structural optimization is very typical of sectors like mechanical, automotive engineering, while in architecture it is a less used approach that however could give new possibilities to performative design. Topology Optimization, one of its most developed sub-methods, is based on the idea of optimization of material densities within a given design domain, along with least material used and wasted energy. In the text is provided a description of TO methods and the principles of their utilization. The process of topology optimization of microstructures of cellular materials is represented and illustrated, emphasizing the all-important criteria and parameters for structural design. A specific example is given of the research at ACTLAB, ACB Dept, Politecnico di Milano, of performative design with lattice cellular solid structures for architecture.

Fixture Configuration Design Based on Topology Optimization

1999 ◽  
Author(s):  
Jinling Liu ◽  
S. Jack Hu ◽  
Jingxia Yuan
Keyword(s):  
Topology Optimization ◽  
Optimization Techniques ◽  
Configuration Design ◽  
Design Domain ◽  
Material Distribution ◽  
Configuration Optimization ◽  
New Approach ◽  
Density Method ◽  
Continuous Density ◽  
Fixture Configuration

Abstract This paper proposes a new approach to fixture configuration optimization. This approach is based on the concept of topology optimization of mechanical structures. Unlike existing techniques of fixture configuration optimization, this approach yields the optimal fixture topology by optimizing the fixture material distribution in a design domain, which surrounds the workpiece to be supported. Two methods, discrete density method and continuous density method, are used to optimize fixture topology. Application examples are given to validate these methods and to further illustrate the idea of fixture topology optimization. Compared with existing fixture configuration optimization techniques, the approach presented in this paper optimizes the fixture topology, rather than the number and/or placement of locators.

scholarly journals Topology optimization incorporating external variables with metamodeling

2020 ◽  
Vol 62 (5) ◽  
pp. 2455-2466
Author(s):  
Shun Maruyama ◽  
Shintaro Yamasaki ◽  
Kentaro Yaji ◽  
Kikuo Fujita
Keyword(s):  
Topology Optimization ◽  
Design Problem ◽  
Optimization Problem ◽  
Design Domain ◽  
Material Distribution ◽  
Topology Optimization Problem ◽  
Design Variables ◽  
External Variables ◽  
Multi Level ◽  
Dependence Relationship

Abstract The objective of conventional topology optimization is to optimize the material distribution for a prescribed design domain. However, solving the topology optimization problem strongly depends on the settings specified by the designer for the shape of the design domain or their specification of the boundary conditions. This contradiction indicates that the improvement of structures should be achieved by optimizing not only the material distribution but also the additional design variables that specify the above settings. We refer to the additional design variables as external variables. This paper presents our work relating to solving the design problem of topology optimization incorporating external variables. The approach we follow is to formulate the design problem as a multi-level optimization problem by focusing on the dominance-dependence relationship between external variables and material distribution. We propose a framework to solve the optimization problem utilizing the multi-level formulation and metamodeling. The metamodel approximates the relationship between the external variables and the performance of the corresponding optimized material distribution. The effectiveness of the framework is demonstrated by presenting three examples.

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